Problem: What is the measure, in units, of the hypotenuse of a right triangle with leg lengths of 75 and 100 units?
Explanation: Using the Pythagorean Theorem, \begin{align*}
d&=\sqrt{75^2+100^2} \\
&=\sqrt{25^2(3^2+4^2)} \\
&=25\sqrt{3^2+4^2} \\
&=25\sqrt{9+16} \\
&=25\sqrt{25} \\
&=25 \cdot 5 \\
&=\boxed{125} \text{units}
\end{align*}